 A bit of the idea on what is the state of the art on the subject because this is a research area which is open for research and people should contribute, a lot of things are to be answered. I am sure that state of the art tells you that you need not to conduct any of the conventional experiments in the laboratory in today's world because people have no time. And look at the size of the infrastructure which is being developed, you know, thousands of acres, thousands of kilometers and also one of the days when people used to take out the samples and bring them to the laboratory and test them. The contemporary thought process is that I should be getting in C2 properties and which are more reliable and you know, this is the fashion. So all this started since 1736 when Coulomb came out with the theory which is known as Coulomb's law, Maxwell, Frick, Archie. So Archie's factor that is formation factor is a function of porosity is what is being used by the guys who are in the realm of geotechnical engineering and those who are geophysicists. So this formation factor basically tells you what is the contrast of the electrical conductivity, perpendicular to the plane of the deposit and parallel to the plane of deposits, your K H upon K V. Now this concept is being utilized in understanding how the formations are created and whether these formations should be bearing minerals, petroleum or not. So if you get a chance to work in the petroleum geophysics, you will find that formation factor is utilized there a lot which is the electrical resistivity of the saturated soil divided by the electricity of pore fluid and this is the function of the porosity. There are people who have done a lot of studies since 1933 it has picked up this subject. People have worked in the frequency ranges of 100 to 10 megahertz, kilohertz to megahertz, megahertz range, 20 megahertz to 1 gigahertz range and the soil properties which have been determined are water content, soil structure, particle orientation, electrolyte effect, determination of water content, relative density and soil liquefaction. So this motivated us to take research in this area and if you further look at the list, you will try to see that you will you might find that people have been very ambitious and they have been talking about the clay fraction directly as a function of electrical property porosity, conductivity of the clay, what is electrical dispersion in soils for different applications and even some people have worked on the permeability of the soils. So having a relook at the electrical properties of geomaterials, as we discussed the conductivity and dielectric constant are the two major parameters which are used for defining the state of the material and conductivity comes because of the movement of the charges alright. A dielectric constant is a measure of the capacity of the material to reduce the strength of an electric field and to behave like an insulator. Here we talk about the variation of the electrical properties as a function of frequency of AC and this is what is known as dispersion of electrical properties or dielectric dispersion in the material. So this part I have already discussed that the electrical connection in the moist geomaterials is more you know and we have talked about the polarization also when you apply the voltage across the sample in a electrodes they get oppositely charged. We use here the concept of lossy dielectric material, we treat soil as a lossy dielectric material that means there are some losses of the storage of the charges takes place through the soils. So dielectric constant of the permittivity is a function of frequency and we define K as C into D upon A into epsilon naught. Capacitance is K into A into epsilon naught upon D. So what about the dielectric constant? So dielectric constant is epsilon upon epsilon naught, this is the material permittivity earlier I used this term with ES that was for the soils. Now epsilon could be any material and epsilon naught is the permittivity of the free space. We can represent K in two parts that is the real and imaginary. So K is the real part minus J into imaginary part of the dielectric constant. So this is where the interpretation of the measurement of electrical properties starts, impedance analysis starts. So if I define the dielectric constant as a combination of real part of dielectric constant and imaginary part of the dielectric constant, this is the composite function. What we do is we plot many times real against the imaginary part to decipher the information. I will show you how. So before we go into that a bit on the ohmic conduction of geomaterials all of you know that the flow of current follows the ohms law which is because of the ionic movement and we define current equal to resistivity into V, clear? So we write sometimes as V equal to I into R where R is 1 upon sigma. So this becomes the resistivity or resistance is R. So these are the factors which influence the electrical conduction, void ratio, degree of saturation, shape, size and orientation, pore structure and nature of the pore fluid and its conductivity. As I said earlier unless the grains are charged the surface conductivity is ignored. What you will realize is that ohmic conduction through pore solution is very easy but ohmic conduction through the soils and the grains is going to be very complicated and very soon you will realize this. The reason is when we deal with the fine-grained soils there are double layer formation DDL we call it the diffuse double layer and that is a consortium of different types of ions on the clay platelets. So there is lot of interference which takes place when you measure the electrical properties of geomaterials particularly when they are fine-grained because of double layer formation. So these are the basics of the impedance that when we measure the resistance by using DC current we call it as a resistance. However when we measure the resistance by using AC current this becomes impedance and I can define impedance Z as V as a function of time upon I as a function of time which is nothing but V cos of omega t upon I cos of omega t minus delta. This is the lag behind between the voltage and the current. So when you plot voltage and current together there is a time lag we can define this term as r minus jx in the complex form alright. So r becomes the real part of the resistance and x becomes the imaginary part of the resistance. So whenever we measure the impedance of the samples this impedance can be represented in combination of real and imaginary parts and then these real and imaginary parts can be utilized to decipher lot of information from the geomaterials. So these are the basic models which we use. You have studied the RC circuits and all in your engineering soils can be represented as a RC material a material which shows resistance and capacitance. So this is the equivalence between the geomaterial or the soils and their electrical circuits alright. So these are the components of resistance, inductance and capacitance which can be utilized for defining their impedance. Remember impedance is the resistance and admittance is the conductance or inverse of the impedance. So you must have come across these terms when you deal with the resistors the impedances are when you deal with the inductors this is j omega l and when you deal with the capacitors this is minus 1 upon j omega c. So these components can be fitted to describe the state of the soils and I hope you can realize that if I want to find out the total impedance I can sum up the resistances and when I do it for parallels then I have to sum up all the admittance of the material. So one of my master's students started working in these complicated topic his name is Azaz Masood Bhatt and he published two very impactful papers on electrical characterization of geomaterials which have become landmark papers. He has created this impedance cell the concept is simple you take a small you know rectangular box and this box is standing on a base plate and there are two electrodes which are plate electrodes which are fitted inside and this box can be used for finding out the impedance of the sands and when you are dealing with the liquids then you can use this type of a setup where the liquid can be contained in the cell and there is a top cover and there are two electrodes which are embedded inside the cell. So both systems can be utilized and this is how the setup looks like. What we are doing here is we are measuring the volumetric moisture content of the sample also along with its impedance. So this is the impedance cell we are measuring the impedance of the sand and the moisture content. This is the setup which is used for obtaining the impedance of the samples this is what is known as impedance analyzer. One interesting thing is that the sample itself can be modeled as a combination of RC alright. So if I consider this specimen and these two electrodes I can develop an equivalent circuit like this. So the central portion is of the specimen which is represented as a combination of capacitance and resistance and the two plates of the electrodes are represented as again RC circuit. Now if you plot them on a scale which is known as a nixed plot there are different ways of plotting this data of the complex electronic circuits. So if you see here this is Z prime which is the real part of the resistance and this is the imaginary part of the resistance when you plot the results which you get from this you can get circles and these circles describe the state of the material. So as the frequency increases it tends to infinity very high gigahertz values if you are using the resistance offered by the sample would be less. So this is the very state of the art thing which we are doing right now and we are trying to capture the response of geomaterials and the mechanisms which happen in them by capturing these type of results and showing that how the phases are getting formed and disappear. We did lot of experiments on soils of different types sands and just to show you how the results vary the real part worth imaginary part. I am not going into the details of how the analysis results is done just my intention is to show you how these results can be utilized for characterizing the geomaterials. We use the Z view software and the best way to analyze a soil mass would be to create a simple RC circuit. So what it shows here is if I include the response of theoretical models on the experimental results these are the experimentally obtained results of the soil sample which we are analyzing and if I fit an equivalent circuit to this a simple RC will give you lot of deviation from the experimental results that means you need to refine your circuits. I hope you will find it very useful and this is a very complicated process where you keep on generating the equivalent circuits of the soils and the geomaterials and keep on mapping them over here. So starting from a simple RC circuit what we have done is we have added a resistance to the RC circuit and with this what has happened is the results are at least bound by the experimental results we are not very happy with that. So we have included one constant phase element I do not know whether you remember or not in your electronics course they must have talked about the CPEs constant phase elements which maintain the phase of the system constant. So by introducing a constant phase element we realize that the results are quite matchable and then we did further manipulation to come out with an equivalent circuit for the soils which looks like this. So this is the electrode, this is the electrode in which the sample is encased. So that means the soil sample has been represented by two resistances and one capacitor of what is known as CPE constant phase element. Now you can reply or get the answers to the type of question which you have been asking any process which happens in the soil mass will get reflected if I measure R2, R4 and Cp2 and that is how I can say that what is changing over a period of time. So all the properties of soils have been now imbibed with time and that is the art. So here we have shown how the resistance of the soils changes as far as the grain resistance is concerned the grain boundary two grain sitting next to each other there is a boundary getting created and two grain sitting to each other will also create a sort of a capacitive effect because the pore solution is inside. So we did this type of modelling a lot and then we came out with the analogy of how current flows through the geomaterials all this done by my students Azaz and Dr. Hanumanth Rao. So you can read their papers which have been published. Now if you look at the possibilities of current which is passing through the dry materials there are three possibilities. There is a dry soil so voids have only air one of the possibilities is that from grain to air to grain to air to grain to air this is one of the possibilities. The second possibility is of the current passing is grain to grain, grain to air, grain to grain to grain and so on and third one would be through the voids only. I hope you can realize that deciphering this information from mathematical models is not going to be easy but we are into it and we are trying to develop models which would help you in defining the state of contamination of the soils. We would also try to develop models where you can differentiate between the fine grained soils and the coarse grained soils including their shapes is quite intricate R and D. Differentiating between the saturated state of the material and the unsaturated state of the material is very easy that you can do very quickly by doing this type of modelling. So, this is the micro mechanics of how the current flows through the porous media. So, A to A is the surface of the soil grain which is mainly due to presence of surface charges. If you remember we were talking about what is the difference between the coarse grained particles and the fine grained particles, coarse grained particles do not have surface charge, fine grained particles have surface charge. So, this is one of the differences and we can utilize this concept in differentiating the material without any sieve analysis because you know the sieve analysis and the hydrometer analysis has its own limitations and the problems. The BB path is the soil cluster wherein the soil grains are in contact with each other and the current may flow through the interconnected grains. This type of possibilities are going to be more in case of fine grained materials as compared to coarse grained materials. The third possibility is partly through the soil grains and partly through the air which is present in the whites which is the least likely part due to its high resistance which is offered by the air. So, once you enter into the micro mechanisms of this type this becomes quite complicated. Presently what we are trying to do is we are trying to model the gaseous phases into the soil mass and the bacterial activity into the soil mass. So, for us the bacteria itself becomes a particle and gas molecules would be present into the pores and if I apply pressure and temperature conditions what is going to happen either the gases which are present in the whites would get dissolved in the pore solution clear or there could be crystallization of the water in the form of the ice. So, this becomes a very complicated matrix. The second possibility is when we deal with the partially saturated systems. So, the concepts remain same only thing is we have created a white which is water filled. So, you have the grains of the soils in between there is a white which is full of water to me it appears like a several capacitors which are arranged within the soil mass either in the parallel or series. So, once I do the impedance analysis I come out with the equivalent circuits and there in the equivalent circuits then again I have to model what type of combinations of the resistances capacitance can be possible which would give you the response of a material. So, there are the possibilities of current passing through this AA prime interconnected pores these are all interconnected pores the easiest way for conduction of the current clear particularly if the ionic solution is present in the pores the B is interconnected soil grains only then CC prime is the partly through the connected soil grains and sometimes through the interconnected pores and DD is the grain through the voids which might contain air and the pore solution. The third possibility would be when we have saturated soils. So, I hope you realize now we are trying to attempt characterization of geomaterials based on their saturation which is the genesis of unsaturated soils. So, one of the possibilities is the pore solution continuous pore solution which is present in the soils the easiest way for current to pass through no resistance is being offered much B prime double prime is interconnected soil grains provided the soil grains have good conductivity like fine-grained materials third is the sandwich of the two we have the interconnected soil grains and partly through the pore fluid. So, these type of micro mechanisms have to be studied and they should be developed in the near future. Sir micro organism like when they are present you said the current passing capacity will decrease drastically the micro organism is if present in any phase around the soil grains then organic matter will hinder the process like at that time I was very complicated situation. Yeah the aim is to use these models to determine how degradation in the material is going on and not only the degradation but upgradation also. If we need to find the impedance of fine-grained soils or properties of fine-grained soils then what we will means he employed for sands impedance of sand he found. So, if we need to found the impedance of clays or fine-grained soils. So, what change will occur? What change will occur? How will we do? The interference will come. A quick answer to your question is nothing of this sort is going to happen. Measurements can be done. It is like generating a lot of ECGs but if the doctor or the person does not know how to decode the ECGs what ECGs are going to do. I hope you can understand my point. So, measurement of the properties is not an issue. You can just pack the sample in the cell and then you can measure something. The million dollar question is how to create a mechanism out of it and how to decipher the results so that these results can be utilized by people who are in the field of monitoring instrumentation and micro mechanisms.